1
Peizhao Wang
2022/7/22
#library a bunch of packages we may (or may not) use - install them first if not installed already.
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## * Use suppressPackageStartupMessages() to eliminate package startup messageslibrary(usethis)## Warning: 程辑包'usethis'是用R版本4.1.2 来建造的library(corrr)## Warning: 程辑包'corrr'是用R版本4.1.2 来建造的LondonWardProfiles <- read_csv(here::here('data','out2.csv'),
na = c("", "NA", "n/a"),
col_names = TRUE)## New names:
## * `` -> ...1## Rows: 625 Columns: 18## -- Column specification --------------------------------------------------------
## Delimiter: ","
## chr (1): New Code
## dbl (17): ...1, Children_Poverty_Rate, E1, E2, E3, E4, E5, E6, HD1, HD2, L1,...##
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.Londonwards <- st_read(here::here("data", "statistical-gis-boundaries-london", "statistical-gis-boundaries-london","ESRI", "London_Ward_CityMerged.shp"))## Reading layer `London_Ward_CityMerged' from data source
## `D:\Master\Dissertation\data expplore\1\data\statistical-gis-boundaries-london\statistical-gis-boundaries-london\ESRI\London_Ward_CityMerged.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 625 features and 7 fields
## Geometry type: POLYGON
## Dimension: XY
## Bounding box: xmin: 503568.2 ymin: 155850.8 xmax: 561957.5 ymax: 200933.9
## Projected CRS: OSGB 1936 / British National Grid#check all of the columns have been read in correctly
Datatypelist <- LondonWardProfiles %>%
summarise_all(class) %>%
pivot_longer(everything(),
names_to="All_variables",
values_to="Variable_class")
Datatypelist## # A tibble: 18 x 2
## All_variables Variable_class
## <chr> <chr>
## 1 ...1 numeric
## 2 New Code character
## 3 Children_Poverty_Rate numeric
## 4 E1 numeric
## 5 E2 numeric
## 6 E3 numeric
## 7 E4 numeric
## 8 E5 numeric
## 9 E6 numeric
## 10 HD1 numeric
## 11 HD2 numeric
## 12 L1 numeric
## 13 L2 numeric
## 14 O numeric
## 15 P1 numeric
## 16 P2 numeric
## 17 P3 numeric
## 18 Q numeric#merge boundaries and data
LonWardProfiles <- Londonwards%>%
left_join(.,
LondonWardProfiles,
by = c("GSS_CODE" = "New Code"))#let's map our dependent variable to see if the join has worked:
tmap_mode("plot")## tmap mode set to plottingqtm(LonWardProfiles,
fill = "Children_Poverty_Rate",
borders = NULL,
fill.palette = "Blues")
library(corrr)
Correlation <- LonWardProfiles %>%
st_drop_geometry()%>%
dplyr::select(Children_Poverty_Rate,
E1,
E2,
E3,
E4,
E5,
E6,
HD1,
HD2,
L1,
L2,
O,
P1,
P2,
P3,
Q)%>%
correlate() %>%
# just focus on Children_Poverty_Rate
focus(-Children_Poverty_Rate, mirror = TRUE) ##
## Correlation method: 'pearson'
## Missing treated using: 'pairwise.complete.obs'#visualise the correlation matrix
rplot(Correlation)## Don't know how to automatically pick scale for object of type noquote. Defaulting to continuous.
using the stepwise regression dimension reduced data
Regressiondata2<- LonWardProfiles%>%
dplyr::select(Children_Poverty_Rate,
E3,
E4,
E6,
O,
Q)model2 <- LonWardProfiles %>%
lm(Children_Poverty_Rate ~
E3+
E4+
E6+
O+
Q, data =.)
#show the summary of those outputs
tidy(model2)## # A tibble: 6 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 3.01 1.81 1.66 9.65e- 2
## 2 E3 -0.0601 0.0210 -2.87 4.26e- 3
## 3 E4 0.300 0.0407 7.36 5.72e- 13
## 4 E6 0.0663 0.0123 5.40 9.29e- 8
## 5 O 0.915 0.0132 69.2 2.32e-293
## 6 Q 0.0807 0.0180 4.48 8.94e- 6all variables are reliable
glance(model2)## # A tibble: 1 x 12
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.978 0.978 1.64 5429. 0 5 -1191. 2397. 2428.
## # ... with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>tidy(durbinWatsonTest(model2))## # A tibble: 1 x 5
## statistic p.value autocorrelation method alternative
## <dbl> <dbl> <dbl> <chr> <chr>
## 1 1.88 0.112 0.0588 Durbin-Watson Test two.sidedThe Durbin-Watson Test result is not significant.
res <- resid(model2)plot(fitted(model2), res)
The statistic is very close to 2, indicating very small positive autocorrelation.
Because the p-value is less than 0.05, it cannot indicate that there is autocorrelation
droped_London_poverty_merged_file <- LonWardProfiles %>%
drop_na()droped_London_poverty_merged_file_with_residual <- droped_London_poverty_merged_file %>%
mutate(.,res)tmap_mode("view")## tmap mode set to interactive viewingtm_shape(droped_London_poverty_merged_file_with_residual) +
tm_polygons("res",
palette = "RdYlBu")## Variable(s) "res" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.residuals are mostly from -5 to 5, following a normal distribution. Meaning that the regression is feasible.
#calculate the centroids of all Wards in London
coordsW <- droped_London_poverty_merged_file_with_residual%>%
st_centroid()%>%
st_geometry()## Warning in st_centroid.sf(.): st_centroid assumes attributes are constant over
## geometries of xplot(coordsW)
#Now we need to generate a spatial weights matrix
#(remember from the lecture a couple of weeks ago).
#We'll start with a simple binary matrix of queen's case neighbours
LWard_nb <- droped_London_poverty_merged_file_with_residual %>%
poly2nb(., queen=T)
#or nearest neighbours
knn_wards <-coordsW %>%
knearneigh(., k=4)
LWard_knn <- knn_wards %>%
knn2nb()
#plot them
plot(LWard_nb, st_geometry(coordsW), col="red")
plot(LWard_knn, st_geometry(coordsW), col="blue")
test Moran’s I to check spatial autocorrelation
Lward.lw <- LWard_nb %>%
nb2listw(., style="C")I_LWard_Global_Density <- droped_London_poverty_merged_file_with_residual %>%
pull(Children_Poverty_Rate) %>%
as.vector()%>%
moran.test(., Lward.lw)
I_LWard_Global_Density##
## Moran I test under randomisation
##
## data: .
## weights: Lward.lw
##
## Moran I statistic standard deviate = 25.243, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.5841638337 -0.0016025641 0.0005384643The statistic value is more close to 1 other than -1. This means there are cluster with similar values.
#create a spatial weights matrix object from these weights
Lward.queens_weight <- LWard_nb %>%
nb2listw(., style="W")
Lward.knn_4_weight <- LWard_knn %>%
nb2listw(., style="W")Queen <- droped_London_poverty_merged_file_with_residual %>%
st_drop_geometry()%>%
dplyr::select(res)%>%
pull()%>%
moran.test(., Lward.queens_weight)%>%
tidy()run a spatially-lagged regression model with a queen’s case weights matrix
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## spBreg_lag, spBreg_sac, stsls, subgraph_eigenw, trWslag_dv_model2_queen <- lagsarlm(Children_Poverty_Rate ~
E3+
E4+
E6+
O+
Q,
data = droped_London_poverty_merged_file_with_residual,
nb2listw(LWard_nb, style="C"),
method = "eigen")
#what do the outputs show?
tidy(slag_dv_model2_queen)## # A tibble: 7 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 rho 0.000531 0.00768 0.0691 9.45e- 1
## 2 (Intercept) 3.02 1.81 1.67 9.52e- 2
## 3 E3 -0.0604 0.0211 -2.86 4.27e- 3
## 4 E4 0.299 0.0407 7.36 1.85e-13
## 5 E6 0.0663 0.0122 5.42 5.90e- 8
## 6 O 0.915 0.0136 67.1 0
## 7 Q 0.0804 0.0183 4.39 1.12e- 5summary(slag_dv_model2_queen)##
## Call:lagsarlm(formula = Children_Poverty_Rate ~ E3 + E4 + E6 + O +
## Q, data = droped_London_poverty_merged_file_with_residual,
## listw = nb2listw(LWard_nb, style = "C"), method = "eigen")
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.01098 -0.95980 -0.03594 0.94120 6.95888
##
## Type: lag
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.021435 1.810558 1.6688 0.095160
## E3 -0.060363 0.021123 -2.8577 0.004267
## E4 0.299345 0.040677 7.3590 1.854e-13
## E6 0.066251 0.012220 5.4217 5.903e-08
## O 0.914510 0.013621 67.1379 < 2.2e-16
## Q 0.080438 0.018309 4.3934 1.116e-05
##
## Rho: 0.00053079, LR test value: 0.0048011, p-value: 0.94476
## Asymptotic standard error: 0.0076811
## z-value: 0.069104, p-value: 0.94491
## Wald statistic: 0.0047754, p-value: 0.94491
##
## Log likelihood: -1191.468 for lag model
## ML residual variance (sigma squared): 2.6507, (sigma: 1.6281)
## Number of observations: 625
## Number of parameters estimated: 8
## AIC: 2398.9, (AIC for lm: 2396.9)
## LM test for residual autocorrelation
## test value: 10.789, p-value: 0.0010208glance(slag_dv_model2_queen)## # A tibble: 1 x 6
## r.squared AIC BIC deviance logLik nobs
## <dbl> <dbl> <dbl> <dbl> <dbl> <int>
## 1 0.978 2399. 2434. 1657. -1191. 625#run a spatially-lagged regression model # Using the 4 nearest neighbours instead of just considering all adjcent zones in the spatial weights matrix
#run a spatially-lagged regression model
slag_dv_model2_knn4 <- lagsarlm(Children_Poverty_Rate ~
E3+
E4+
E6+
O+
Q,
data = droped_London_poverty_merged_file_with_residual,
nb2listw(LWard_knn,
style="C"),
method = "eigen")
#what do the outputs show?
tidy(slag_dv_model2_knn4)## # A tibble: 7 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 rho 0.0234 0.0125 1.87 6.10e- 2
## 2 (Intercept) 3.35 1.81 1.86 6.34e- 2
## 3 E3 -0.0662 0.0211 -3.13 1.74e- 3
## 4 E4 0.289 0.0409 7.06 1.66e-12
## 5 E6 0.0642 0.0122 5.25 1.55e- 7
## 6 O 0.903 0.0144 62.7 0
## 7 Q 0.0731 0.0184 3.98 6.87e- 5glance(slag_dv_model2_knn4)## # A tibble: 1 x 6
## r.squared AIC BIC deviance logLik nobs
## <dbl> <dbl> <dbl> <dbl> <dbl> <int>
## 1 0.978 2395. 2431. 1647. -1190. 625The Spatial Error Model with queen’s case wight matrix
sem_model2 <- errorsarlm(Children_Poverty_Rate ~
E3+
E4+
E6+
O+
Q,
data = droped_London_poverty_merged_file_with_residual,
nb2listw(LWard_nb, style="C"),
method = "eigen")
tidy(sem_model2)## # A tibble: 7 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 2.05 1.96 1.05 2.96e- 1
## 2 E3 -0.0495 0.0229 -2.17 3.03e- 2
## 3 E4 0.322 0.0455 7.08 1.47e-12
## 4 E6 0.0695 0.0129 5.36 8.15e- 8
## 5 O 0.907 0.0143 63.5 0
## 6 Q 0.0846 0.0196 4.31 1.60e- 5
## 7 lambda 0.196 0.0628 3.12 1.83e- 3glance(sem_model2)## # A tibble: 1 x 6
## r.squared AIC BIC deviance logLik nobs
## <dbl> <dbl> <dbl> <dbl> <dbl> <int>
## 1 0.978 2389. 2425. 1620. -1187. 625sem_model2_2 <- errorsarlm(Children_Poverty_Rate ~
E3+
E4+
E6+
O+
Q,
data = droped_London_poverty_merged_file_with_residual,
nb2listw(LWard_knn, style="C"),
method = "eigen")
tidy(sem_model2_2)## # A tibble: 7 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 1.69 1.96 0.861 3.89e- 1
## 2 E3 -0.0446 0.0228 -1.95 5.08e- 2
## 3 E4 0.325 0.0453 7.16 7.87e-13
## 4 E6 0.0692 0.0130 5.33 9.72e- 8
## 5 O 0.907 0.0142 63.7 0
## 6 Q 0.0847 0.0198 4.27 1.96e- 5
## 7 lambda 0.193 0.0553 3.49 4.84e- 4glance(sem_model2_2)## # A tibble: 1 x 6
## r.squared AIC BIC deviance logLik nobs
## <dbl> <dbl> <dbl> <dbl> <dbl> <int>
## 1 0.978 2387. 2423. 1613. -1186. 625run a lag model if you identify spatial autocorrelation in the dependent variable (closer spatial units have similar values) with Moran’s I.
The Lagrange multiple tests
Test with queen’s case
library(spdep)
Lward.queens_weight_ROW <- LWard_nb %>%
nb2listw(., style="W")
lm.LMtests(model2, Lward.queens_weight_ROW, test = c("LMerr","LMlag","RLMerr","RLMlag","SARMA"))##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = Children_Poverty_Rate ~ E3 + E4 + E6 + O + Q, data
## = .)
## weights: Lward.queens_weight_ROW
##
## LMerr = 8.9109, df = 1, p-value = 0.002835
##
##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = Children_Poverty_Rate ~ E3 + E4 + E6 + O + Q, data
## = .)
## weights: Lward.queens_weight_ROW
##
## LMlag = 0.77683, df = 1, p-value = 0.3781
##
##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = Children_Poverty_Rate ~ E3 + E4 + E6 + O + Q, data
## = .)
## weights: Lward.queens_weight_ROW
##
## RLMerr = 8.2233, df = 1, p-value = 0.004136
##
##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = Children_Poverty_Rate ~ E3 + E4 + E6 + O + Q, data
## = .)
## weights: Lward.queens_weight_ROW
##
## RLMlag = 0.089295, df = 1, p-value = 0.7651
##
##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = Children_Poverty_Rate ~ E3 + E4 + E6 + O + Q, data
## = .)
## weights: Lward.queens_weight_ROW
##
## SARMA = 9.0002, df = 2, p-value = 0.01111Test with KNN
Lward.knn_weight_ROW <- LWard_knn %>%
nb2listw(., style="W")
lm.LMtests(model2, Lward.knn_weight_ROW, test = c("LMerr","LMlag"))##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = Children_Poverty_Rate ~ E3 + E4 + E6 + O + Q, data
## = .)
## weights: Lward.knn_weight_ROW
##
## LMerr = 12.323, df = 1, p-value = 0.0004475
##
##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = Children_Poverty_Rate ~ E3 + E4 + E6 + O + Q, data
## = .)
## weights: Lward.knn_weight_ROW
##
## LMlag = 3.5595, df = 1, p-value = 0.05921